Is there a particular name for this "picture of a baby seal in the comments section of facebook" of this image? I know there is "photo comment" but it doesn't point out that it is a cropped picture from the original.

Thumbnails are reduced-size versions of pictures, used to help in recognizing and organizing them, serving the same role for images as a normal text index does for words. In the age of digital images, visual search engines and image-organizing programs normally use thumbnails, as do most modern operating systems or desktop environments, such as Microsoft Windows, Mac OS X, KDE (Linux) and GNOME (Linux).

While the definition above doesn't exclude it, thumbnails tend to be smaller ("reduced-size") versions of the whole image, not a cropped part of an image.
– TripeHoundDec 16 '15 at 13:03

2

Most OSes/platforms do it automatically but there are tools and techniques to choose what part of the image/video you want to display as your thumbnail.
– BiscuitBoyDec 16 '15 at 13:21

The "used to help in recognizing and organizing them" part of the definition makes it irrelevant to the OP as it is quite obvious that cropped image in the comment serves neither of the mentioned purposes.
– n0rdDec 16 '15 at 19:36

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While it is possible to select a region of an image to use as a thumbnail in some tools, the thumbnail itself is normally expected to be representative of the original, as @TripeHound suggests. In the example given in the Q, the use of "thumbnail" would be an extreme and misleading example.
– Chris HDec 16 '15 at 22:37

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A thumbnail often highlights the focal point of a larger photo that you want to convey based on context. Eg. Picking out one face from a group of people. The detail picked out can vary according to use and often there can be multiple thumbnails highlighting different parts of the pic. Eg. each person. So I think @TripeHound the idea that it must represent the whole photo is outdated thinking and does not match current real world usage of the term.
– JamesRyanDec 18 '15 at 10:39

To me "an edit" refers to the act or the change itself, not so much the product (unless as journalistic jargon for "version"). I also associate it with text more than with visual arts.
– GossarDec 16 '15 at 15:02

4

And "to expunge, eliminate" strikes me as a verb, not a noun.
– GossarDec 16 '15 at 15:18

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I also dispute this, with "edit" more commonly (in my experience) referring to a manipulation of an image as opposed to only selecting a sub-set of a larger image ('cropping').
– kwahDec 16 '15 at 17:40

@kwah when I open my Microsoft Office Picture Manager there is a tab called edit and the tool for cropping and/or resizing an image appears alongside other different tools.
– Mari-Lou ADec 16 '15 at 20:39

Zoom. Lots of valid answers here but I'd call it a "zoom". The precedent, particularly in popular Web usage and where the cropped image appears in proximity to the original is not uncommonly used as a kind of reaction GIF or more specifically a "zoom meme".